1

Suppression of Ferromagnetic Double Exchange by Vibronic

Phase Segregation

F. Rivadulla1, M. Otero-Leal

2, A. Espinosa

3, A. de Andrés

3, C. Ramos

4, J. Rivas

2, J. B.

Goodenough5

1Physical-Chemistry and

2Applied Physics Departments, University of Santiago de Compostela, 15782

Santiago de Compostela, Spain.

3Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas,

Cantoblanco, E-28049 Madrid, Spain

4Centro Atómico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Rio Negro, Argentina

5Texas Materials Institute, ETC 9.102, The University of Texas at Austin, 1 University Station, C2201,

Austin, Texas 78712, USA

From Raman spectroscopy, magnetization, and thermal-expansion on the system

La2/3(Ca1-xSrx)1/3MnO3, we have been able to provide a quantitative basis for the

heterogeneous electronic model for manganites exhibiting colossal magnetoresistance

(CMR). We construct a mean-field model that accounts quantitatively for the measured

deviation of TC(x) from the TC predicted by de Gennes double exchange in the adiabatic

approximation, and predicts the occurrence of a first order transition for a strong coupling

regime, in accordance with the experiments. The existence of a temperature interval

TC<T<T* where CMR may be found is discussed, in connection with the occurrence of an

idealized Griffiths phase.

2

The La1-ySryMnO3 perovskite system with y>0.17 has been shown1 to be a de

Gennes2 double-exchange ferromagnet; it contains itinerant electrons in a narrow σ

* band

of e-orbital parentage coexisting with a localized t3 configuration at the high-spin

Mn4+

/Mn3+

mixed-valent MnO3 array. The adiabatic approximation, which assumes the

electrons and the ions make a separate contribution to the total energy of the MnO3 array,

is applicable to the itinerant electrons of La0.7Sr0.3MnO3. On the other hand, early

experiments3 on the system (La1-xPrx)0.7Ca0.3MnO3 showed a remarkable decrease of TC

and a colossal magnetoresistance (CMR) effect above TC that increased with decreasing x

until a transition to an orbitally ordered, antiferromagnetic-insulator phase. This striking

evolution with x of magnetic and transport properties was interpreted4 to result from the

stabilization of phase fluctuations of itinerant and localized electronic regions due to

lattice instabilities associated with a first-order transition at the crossover from polaronic

to itinerant electron behavior. Although evidences for the phase fluctuations and their

responsibility for the CMR phenomenon have been well-documented, a quantitative

description of the evolution of TC with x has been lacking. In order to fill this gap, we

have undertaken a systematic study of the ferromagnetic system La2/3(Ca1-xSrx)1/3MnO3

which shows a similar CMR phenomenon and variation of TC with x. The study allows us

to account quantitatively for the evolution of TC with x using experimentally determined

parameters. We demonstrate that dynamic phase segregation into hole-rich itinerant-

electron regions and hole-poor localized-electron regions, results from a breakdown of

the adiabatic approximation for the itinerant electrons and suppresses the conventional

double-exchange coupling. Our model provides an original scenario to understand the

3

first order nature of the magnetic phase transition in a situation in which TC is suppressed,

which could be of general applicability to other systems.

0.00 0.25 0.50 0.75 1.00200

250

300

350

400

TC(adiabatic)

TC

Tt

T (

K)

x

Figure 1: (solid circles): evolution of TC with x across the series La2/3(Ca1-xSrx)1/3MnO3

determined experimentally. (open triangles): Pnma↔ R 3 c structural transition

temperature determined experimentally. (open squares): evolution of TC with x calculated

from a free-electron DE model (equation (1)), as explained in the text. (solid squares):

calculated TC with the mean-field model coupled to the lattice proposed in this work as

explained in the text.

Fig. 1 shows the experimental magnetic and structural phase diagram for

La2/3(Ca1-xSrx)1/3MnO3. The progressive introduction of Ca in this system increases the

bending of the (180°-φ) Mn-O-Mn bond angle,5 which induces a phase transition from

rhombohedral (R 3 c) to orthorhombic (Pbnm) symmetry at a room-temperature critical

concentration xt≈0.45. In the adiabatic approximation, the ferromagnetic Curie

temperature TC is proportional to the double-exchange energy parameter

J ∼ c(1−c)zbcosφcos(θij/2) (1)

4

where c and (1−c) are the fraction of Mn3+

and Mn4+

states at the z nearest neighbors to

which an electron can hop from Mn3+

to Mn4+

, b is the conventional spin-independent

energy-transfer integral, and θij is the angle between the spins on the two ions where

electron transfer occurs.6 The open squares in Fig. 1 (TC(adiabatic)) are an estimation of

the TC vs. cosφ to be expected for a homogenous system of itinerant σ* electrons as

extrapolated from the value of TC for La2/3Sr1/3MnO3. The deviation of the experimental

dTC/dx from this extrapolation is less than 4% in the rhombohedral phase; but in the

orthorhombic phase the deviation is much more pronounced. For the end member

La2/3Ca2/3MnO3 (x=0), the discrepancy in TC is nearly 100 K. Inclusion of the effect of a

long-range stress field7 or of the variance in the A-site cation radii

8 cannot explain this

strong suppression of TC or its variation with x. The more rapid decrease of TC with x

from the extrapolated value in the orthorhombic phase is suggestive that the adiabatic

approximation for the narrow σ* band breaks down more rapidly in this phase than in the

rhombohedral phase. This can be qualitatively understood: narrowing of the adiabatic σ*

bandwidth W0 ∼ bcosφ by increasing the bending φ of the (180°-φ) Mn-O-Mn angles

increases the time τh ∼h/W0 for an electron to tunnel from a Mn3+

to a Mn4+

ion, and the

adiabatic approximation is only valid for τh<ωo−1

, where ωo−1

is the period of the optical-

mode vibration of the MnO3 array that would localize the electron as a small polaron (or

as a two-manganese Zener polaron). Where a τh ≈ ωo−1

is approached, τh increases with

the depth of the polaronic trap state, and this trap state is deepened by a Jahn-Teller

deformation (orbital ordering) of the site. The orthorhombic crystal symmetry allows a

Jahn-Teller deformation whereas rhombohedral symmetry does not support lifting of the

e-orbital degeneracy. Zhao et al.9 reported a large oxygen isotope effect on TC of

5

orthorhombic manganites where long-range Janh-Teller distortions are present.

Increasing the mass of the oxygen isotope decreases the frequencies of the Mn-O-Mn

modes and TC decreases. If on cooling through TC the transition was from a global

polaronic phase (τh>ωo−1

) to a global itinerant electronic phase (τh<ωo−1

), then the

exchange of 18

O for 16

O should favor the itinerant electron phase. The decrease of TC by

18O/

16O exchange was interpreted

4 as an evidence of the two-phase character of the

electronic system. The dramatic changes in TC by Mn-O-Mn angle variation should be

then caused by the dependence of volume fraction of the polaronic/itinerant phases on the

ωo(φ). In order to probe whether such a relation exists, we measured with Raman

spectroscopy the evolution with x of the frequency of the oxygen vibrations

perpendicular to a Mn-O-Mn bond.10

Fig. 2 shows a linear decrease in this frequency, i.e.

an increase in ωo−1

, with increasing Sr.

200 300 400 500

200 210 220 230 240250

300

350

Inte

nsity

(a.u

.)

Raman shift (cm-1)

TC(K

)

Raman shift (cm-1)

6

Figure 2: Raman spectra for La2/3(Ca1-xSrx)1/3MnO3 at 100 K. From bottom to top x=0,

0.20, 0.30, 0.40, 0.50, 0.60, 0.65, 1. The last two, plotted with open circles, belong to the

R 3 c group at this temperature (note that at 100 K the orthorhombic-to-rhombohedral

transition occurs for x≈0.6, see Fig. 1). Inset: Dependence of the TC with the frequency of

the Mn-O-Mn tilting mode.

The similarity of dTC/dx and dωo−1

/dx is remarkable, providing a solid basis for

the heterogeneous model. A system which is at a crossover from polaronic to itinerant

electronic behavior is intrinsically unstable relative to segregation into hole-rich,

itinerant-electron regions with τh < ωo−1

and hole-poor polaronic regions with τh > ωo−1

.

Since the phase segregation is dynamic, the measured ωo reflects a weighted average of

the two frequencies for the two volume fractions; the Raman peak is not split into two

peaks as would be expected for classic, static phase segregation. However, the peak shifts

to higher frequencies as the volume fraction of the polaronic phase increases.11

With this

interpretation of the Raman data of Fig. 2, we conclude that the deviation of TC from the

predicted by the adiabatic approximation at low x reflects a continuous growth of the

volume fraction of the polaronic phase as φ increases. In the polaronic phase, τh becomes

too long relative to the spin reorientation time (τh>τr) for the double-exchange

mechanism to be operational. In the system La1-xSrxMnO3, TC was reported to increase

rapidly with pressure for the interval 0.1<x<0.2.12

, where a short-range dynamic ordering

at Mn(III) ions introduces a modified version of Zener’s13

ferromagnetism. On crossing

to the high-pressure itinerant side through a first-order transition, de Gennes model is

restored and dTC/dP decreases. These results are in perfect accordance with our

experimental observations.

7

Fig. 3 shows the temperature dependence of ZFC and FC curves for x = 0.5; this

sample undergoes an orthorhombic to rhombohedral transition at Tt = 225 K < TC. Both

the splitting of the ZFC and FC curves in the orthorhombic phase as well as its lower

magnetization relative to that of the rhombohedral region, are clear indications of an

inhomogeneous magnetic system, even well below TC. This, along with the departure of

TC from the adiabatic prediction and the Raman experiment, strongly support a dynamic

coexistence of two phases in the orthorhombic phase, 14

the itinerant-electron volume

fraction increasing in an applied magnetic field. On the other hand the behavior in the

rhombohedral phase is characteristic of a homogeneous itinerant-electron phase.

0 100 200 300 4000.0

0.1

0.2

0.3FC

ZFC TC

Pbnm R-3c

Tt

La2/3

(Ca0.5

Sr0.5

)1/3

MnO3

M (

µB/M

n)

Temperature (K)

Figure 3: Temperature dependence of the ZFC-FC magnetization curves of x=0.5

measured at 100 Oe.

In order to translate the implications of an heterogeneous electronic model to a

quantitative calculation of TC vs. x, we constructed a mean-field model starting from the

equation of state of a ferromagnet, in which σ(T) = M(T)/M(0), has the form

8

σ = B(y); y = 2zJS2σ/kT (2)

and determine how the double-exchange energy parameter J entering the Brillouin

function B(y) varies with x, i.e. J = J(x). The value of J will depend on the probability

that a τh<ωo−1

to a neighboring Mn4+

ion can occur, i.e. to the volume fraction of itinerant

electrons. If n is the volume fraction of itinerant electrons, then J in equation (2) should

be replaced by

J = nJ0, where n = (1−nJT) (3)

J0 would be the exchange parameter estimated from the adiabatic model and nJT is the

volume fraction of electrons in the polaronic phase.

150 200 250 300 350 400

-1000

0

1000

0.0 0.3 0.6 0.90.0

0.5

1.0

240 320 4000.25

0.50

0.75

1.00

x=1

x=0

∆L

/L

Temperature (K)

R-3cPbnm

JT

-(∆

L/L

) (T

=T

C)

x

x=1

x=0

n

Temperature (K)

Figure 4: Linear thermal expansion of some representative composition of the series

La2/3(Ca1-xSrx)1/3MnO3 (x=0, 0.05, 0.15, 0.25, 0.75, and 1, from left to right). The arrows

mark the TC in the rombohedral samples, where the anomalous contribution due to JT

distortion is suppressed. Upper inset: Relative contribution of the anomalous thermal

expansion at TC. The values where normalized with respect to the contribution at the x=0

sample. Lower inset: Temperature dependence of the number of delocalised electrons, n,

extracted from the thermal expansion experiments as explained in the text.

9

Since the volume of the polaronic phase is greater than that of the itinerant-

electron phase4, a value of nJT can be derived from the deviation of the thermal expansion

from the Grüneisen law. Fig. 4 shows the lattice thermal expansion for different

representative samples of La2/3(Ca1-xSrx)1/3MnO3. For x=0 there is an abrupt departure

from the Grüneisen contribution and an anomalous volume expansion at TC as has been

previously observed by other authors.15

With increasing the Sr content in the

orthorhombic phase, this anomaly decreases and it drops abruptly on entering the

rhombohedral phase where it is nearly fully suppressed (see Fig.4, upper inset). From

numerous studies of the CMR phenomenon it has been established that well-below TC

nearly the entire volume is itinerant, and above TC the CMR compound becomes biphasic

with a sharp change in the relative volume fractions on crossing TC. For this reason, the

values of nJT derived from ∆L/L for x=0 were normalized to vary between 0 at low

temperatures (where almost all the electrons are free) and 2/3 above TC, were the all the

electrons form polarons (there are only 2/3 of the Mn sites occupied by Mn3+

). The

experimental results for n=1-nJT are shown in the lower inset of Fig. 4. The results for all

the samples were normalized with respect to x=0, in order to establish a comparison on

the evolution of the number of localized sites across the series. The continuous departure

of n from 1 as TC is approached from below reflects the progressive appearance of JT-

distorted sites, as it was demonstrated for similar compositions by more local probes.14

The progressive reduction of the volume fraction of the polaronic phase as x increases is

in good accord with the reduction in the frequency of the tilting mode observed by

Raman. The normalized magnetization σ(T) for different values of x according to eqs. (2)

and (3) are shown in Fig. 5. At La2/3Ca1/3MnO3, the continuous renormalization of the

10

double-exchange interaction according to equation (3) reduces TC by up to 30% from the

value of TC for the adiabatic double-exchange mechanism (J=J0). The values of TC(x)

estimated from eq. (2) and the measured n(T,x)=(1−nJT), are shown in Fig. 1 (as the solid

squares) for the series La2/3(Ca1-xSrx)1/3MnO3. An excellent quantitative agreement with

the experimental TC(x) is obtained.

0.0 2.0x107

4.0x107

0

1

2

3

4

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

x=0.05x=0.101.04 T

C

1.03 TC

1.02 TC

1.01 TC

H/M

(O

em

ol/em

u)

M2 (emu/mol)

2

σ

T/TC

Figure 5: Evolution of the reduced magnetization according to eq. (2) and (3). Inset:

Experimental isotherms probing the first-to-sencond order change in the character of the

magnetic phase transition at TC, on going from x=0.05 to x=0.10.

In addition, where the change in nJT(T), i.e. the fraction of sites excluded from the

double-exchange coupling, is very abrupt on approaching TC from below, the model

predicts the occurrence of a first-order magnetic phase transition at TC. The abrupt

renormalization of the exchange parameter on the approach to TC makes it impossible for

the Brillouin function to evolve continuously to zero, and it collapses in a first-order

phase change at the critical point. Therefore, as the volume fraction of the polaronic

11

phase at TC increases, we can anticipate the magnetic-ordering transition at TC will

change from second-order to first-order. From M/H vs. M2 isotherms

16,17 we have

determined experimentally that such a change does indeed occur, and takes place in the

interval 0.05<x<0.10 (see inset of Fig. 5). It should be noted that the metal-to-

semiconducting transition at TC stands up to x=0.5, where it goes metal-to-metal.18

This

shows that the change in the order of the phase transition is not controlled by the nature

of the electronic transition, but by the two-phase character of the system and its relative

volume change at TC.

Previous attempts to account for first-order ferromagnetic-to-paramagnetic transitions

normally relied on a volume dependent exchange interaction in a deformable lattice.19

This ends up with a first-order phase change at a higher temperature than the

corresponding second-order one in the non-deformable lattice, and so they are inadequate

to explain the behavior of manganites, where TC is suppressed. The continuous change in

the effective temperature of the spin-lattice of our model mimics the effect of a

temperature dependent Weiss field coefficient, which also produces a first-order phase

transtition.20

Also Huberman and Streifer21

proposed a similar model to account for the

first-order character of the magnetic transition at TC in MnBi.

In conclusion, we have provided a quantitative basis for the heterogeneous model

4 responsible for the CMR phenomenon. The model can account quantitatively for the

evolution of TC(x) and the change from a first to a second-order magnetic transition at TC.

In addition, in the temperature interval TC<T<TC(adiabatic), the model predicts pockets

of short-range ferromagnetic order to exist in a non-percolative volume fraction of the

itinerant-electron phase; this volume fraction grows in an applied magnetic field to

12

beyond percolation to give the CMR phenomenon. This shares some similarities with the

idealized model proposed by Griffiths22,23

in which an exchange parameter varies with

the probable number of nearest neighbors participating in the exchange interaction.

However Griffiths did not anticipated how this probability might change as a function of

temperature, as it does in manganites. Finally, it should be recognized that Dagotto24

has

independently supported a similar heterogeneous model developed from computational

studies, and that there is a strong similarity between TC(adiabatic) and the temperature

scale represented by T* that he proposed. The analogy between T* and the Griffiths

temperature was also raised by these authors,25

which stressed the relevance of having

two competing orders with similar energies to observe the intrinsically inhomogeneous

regime.

Acknowledgements

We are thankful to E. Dagotto, G. Martinez, J. Mira, J.-S. Zhou for valuable comments

and reading of the manuscript, and C. Hoppe and I. Pardiñas for assistance. We also

thank support from MEC of Spain (MAT2002-11850-E; MAT 2004-05130-C01). FR

acknowledges MCYT of Spain for support under program Ramón y Cajal.

1 J.-S. Zhou, J. B. Goodenough, A. Asamitsu, Y. Tokura, Phys. Rev. Lett. 79, 3234 (1997).

2 P. G. de Gennes, Phys. Rev. 118, 141 (1960).

3 H. Y. Hwang, S-W. Cheong, P. G. Radaelli, M. Marezio, B. Batlogg, Phys. Rev. Lett. 75, 914 (1995).

4 J. B. Goodenough and J.-S. Zhou, “Localizad to Itinerant Electronic Transition in Perovskite Oxides”,

Structure and Bonding vol. 98. Ed. by J. B. Goodenough, Springer 2001. Chapter 2. 5 P.G. Radaelli, G. Iannone, M. Marezio, H. Y. Hwang, S.-W. Cheong, J. D. Jorgensen, D. N. Argyriou,

Rev. Lett. 56, 8265 (1997). 6 J. B. Goodenough, in “The Physics of Manganites”, Ed. by Kaplan and Mahanti, Kluwer

Academic/Plenum Pub. 1999. 7 T. Egami, D. Louca, Phys. Rev. B 65, 94422 (2001).

8 J. P. Attfield, A. L. Kharlanov, J. A. McAllister, Nature 394, 157 (1998).

9 G.-M. Zhao, K. Konder, H. Keller, K. A. Müller, Nature 381, 676 (1996).

10 L. Martín-Carrón, A. de Andrés, M. J. Martínez-Lope, M. T. Casais, J. A. Alonso, Phys. Rev. B 66,

174303 (2002). 11

We have checked that there is a small but visible contribution of the polaronic phase at T>TC to the

bending mode at ≈230 cm-1

. This is in accordance with the results presented in ref. 10.

13

12

J.-S. Zhou, J. B. Goodenough, Phys. Rev. B 62, 3834 (2000). 13

C. Zener, Phys. Rev. 82, 403 (1951). 14

S. J. L. Billinge, Th. Proffen, V. Petkov, J. L. Sarrao, S. Kycia, Phys. Rev. B 62, 1203-1211 (2000). 15

J. M. De Teresa et al., Nature 386, 256 (1997). 16

H. E. Stanley, “Introduction to Phase Transitions and Critical Phenomena”, Oxford University Press,

1971. 17

J. Mira, J. Rivas, F. Rivadulla, C. Vázquez-Vázquez, M. A. López-Quintela, Phys. Rev. B 60, 2998

(1999). 18

Y. Tomioka, A. Asamitsu, Y. Tokura, Phys. Rev. B 63, 024421 (2001). 19

C. P. Bean, D. S. Rodbell, Phys. Rev. 126, 104 (1962). 20

J. S. Smart, Phys. Rev. 90, 55 (1953). 21

B. A. Huberman, W. Streifer, Phys. Rev. B 12, 2741 (1975). 22

R. B. Griffiths, Phys. Rev. Lett. 23, 17 (1969). 23

M. B. Salamon, P. Lin, and S. H. Chun, Phys. Rev. Lett. 88, 197203 (2002). 24

E. Dagotto “Nanoscale Phase Separation and Colossal Magnetoresistance” Springer 2003. 25

J. Burgy, M. Mayr, V. Martín-Mayor, A. Moreo, E. Dagotto, Phys. Rev. Lett. 87, 277202 (2001).